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An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger
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This is a gentle introduction to curves and more specifically algebraic curves. We look at historical aspects of curves, going back to the ancient Greeks, then on the 17th century work of Descartes.
We point out some of the difficulties with Jordan's notion of curve, and move to the polynumber approach to algebraic curves.
The aim is to set the stage to generalize the algebraic calculus of the previous few lectures to algebraic curves.
This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.
Video Content:
00:00 Intro to aglebraic curves
2:16 How to extend elementary calculus to go beyond functions
4:49 Historical notion of a "curve"
7:41 Archimedes' spiral
11:50 Epicycles of Ptolemy
15:13 Cubics a la Newton
18:28 Mechanical curves
22:20 What exactly is a 'curve'?
27:13 'Algebraic curves' by using bipolynumbers
29:28 The Lemniscate of Bernoulli
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Here are the Insights into Mathematics Playlists:
We point out some of the difficulties with Jordan's notion of curve, and move to the polynumber approach to algebraic curves.
The aim is to set the stage to generalize the algebraic calculus of the previous few lectures to algebraic curves.
This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.
Video Content:
00:00 Intro to aglebraic curves
2:16 How to extend elementary calculus to go beyond functions
4:49 Historical notion of a "curve"
7:41 Archimedes' spiral
11:50 Epicycles of Ptolemy
15:13 Cubics a la Newton
18:28 Mechanical curves
22:20 What exactly is a 'curve'?
27:13 'Algebraic curves' by using bipolynumbers
29:28 The Lemniscate of Bernoulli
************************
***********************
Here are the Insights into Mathematics Playlists:
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